Forecasting and Production Planning

Production planning starts with a forecast of demand, then decides how much to make, when, and with what resources.

Forecasting methods

• Simple moving average (n periods): F_{t+1} = (D_t + D_{t−1} + … + D_{t−n+1})/n.
• Weighted moving average: recent periods get larger weights (weights sum to 1).
• Exponential smoothing: F_{t+1} = F_t + α(D_t − F_t) = αD_t + (1 − α)F_t, with 0 < α < 1. Larger α reacts faster to changes; smaller α smooths more.
• Linear regression (trend): D = a + bt with b = (nΣtD − ΣtΣD)/(nΣt² − (Σt)²) and a = D̄ − b t̄.

Forecast errors

With error e_t = D_t − F_t:

• MAD = Σ|e|/n; MSE = Σe²/n.
• Bias (mean error) = Σe/n; a forecast is unbiased if this is near zero.
• Tracking signal = Σe/MAD; values beyond about ±4 mean the forecast should be revised.

Aggregate planning

Matches capacity to demand over the medium term using: changing the workforce (hire/fire), overtime, inventory, subcontracting, or backorders. A level strategy keeps output constant and uses inventory; a chase strategy changes output to follow demand.

MRP

Material requirements planning works backward from the master production schedule using the bill of materials and lead times:

Net requirement = gross requirement − on-hand inventory − scheduled receipts.

Line balancing

For an assembly line with task times tᵢ and cycle time C:

• Cycle time C = available time / required output.
• Minimum number of stations = ⌈Σtᵢ/C⌉.
• Line efficiency = Σtᵢ/(n × C); balance delay = 1 − efficiency.

Worked example

Demand for three months was 100, 120 and 110. The last forecast was 105 with α = 0.2, and actual demand was 110.

• Next forecast = 105 + 0.2 × (110 − 105) = 106.
• 3-month moving average = (100 + 120 + 110)/3 = 110.

Practice